379 research outputs found
Random line graphs and edge-attributed network inference
We extend the latent position random graph model to the line graph of a
random graph, which is formed by creating a vertex for each edge in the
original random graph, and connecting each pair of edges incident to a common
vertex in the original graph. We prove concentration inequalities for the
spectrum of a line graph, as well as limiting distribution results for the
largest eigenvalue and the empirical spectral distribution in certain settings.
For the stochastic blockmodel, we establish that although naive spectral
decompositions can fail to extract necessary signal for edge clustering, there
exist signal-preserving singular subspaces of the line graph that can be
recovered through a carefully-chosen projection. Moreover, we can consistently
estimate edge latent positions in a random line graph, even though such graphs
are of a random size, typically have high rank, and possess no spectral gap.
Our results demonstrate that the line graph of a stochastic block model
exhibits underlying block structure, and in simulations, we synthesize and test
our methods against several commonly-used techniques, including tensor
decompositions, for cluster recovery and edge covariate inference. By naturally
incorporating information encoded in both vertices and edges, the random line
graph improves network inference.Comment: 44 pages total, including supplementary material; 5 figure
Discovering underlying dynamics in time series of networks
Understanding dramatic changes in the evolution of networks is central to
statistical network inference, as underscored by recent challenges of
predicting and distinguishing pandemic-induced transformations in
organizational and communication networks. We consider a joint network model in
which each node has an associated time-varying low-dimensional latent vector of
feature data, and connection probabilities are functions of these vectors.
Under mild assumptions, the time-varying evolution of the constellation of
latent vectors exhibits low-dimensional manifold structure under a suitable
notion of distance. This distance can be approximated by a measure of
separation between the observed networks themselves, and there exist consistent
Euclidean representations for underlying network structure, as characterized by
this distance, at any given time. These Euclidean representations permit the
visualization of network evolution and transform network inference questions
such as change-point and anomaly detection into a classical setting. We
illustrate our methodology with real and synthetic data, and identify change
points corresponding to massive shifts in pandemic policies in a communication
network of a large organization.Comment: 31 pages, 7 figure
Animal Models of Bone Loss in Inflammatory Arthritis: from Cytokines in the Bench to Novel Treatments for Bone Loss in the Bedside—a Comprehensive Review
Throughout life, bone is continuously remodelled. Bone is formed by osteoblasts, from mesenchymal origin, while osteoclasts induce bone resorption. This process is tightly regulated. During inflammation, several growth factors and cytokines are increased inducing osteoclast differentiation and activation, and chronic inflammation is a condition that initiates systemic bone loss. Rheumatoid arthritis (RA) is a chronic inflammatory auto-immune disease that is characterised by active synovitis and is associated with early peri-articular bone loss. Peri-articular bone loss precedes focal bone erosions, which may progress to bone destruction and disability. The incidence of generalised osteoporosis is associated with the severity of arthritis in RA and increased osteoporotic vertebral and hip fracture risk. In this review, we will give an overview of different animal models of inflammatory arthritis related to RA with focus on bone erosion and involvement of pro-inflammatory cytokines. In addition, a humanised endochondral ossification model will be discussed, which can be used in a translational approach to answer osteoimmunological questions
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